Wheat and chessboard problem

The wheat and chessboard problem is a mathematical word puzzle that asks how many grains of wheat would cover a standard chessboard if one grain is placed on the first square and the number doubles on every following square through the sixty-fourth. The total comes to two to the sixty-fourth power minus one, over eighteen quintillion grains, an amount far beyond any real harvest. The puzzle is traditionally framed inside a legend about the invention of chess: a ruler offers the game's inventor, sometimes named Sessa, any reward he names, and the inventor asks only for wheat counted this way, unaware the ruler underestimates the total until his treasury proves unable to pay it. The earliest known written version of the story was recorded in 1256 by the Arab historian Ibn Khallikan, though the mathematical idea behind it is thought to trace back further into Indian mathematical tradition connected to Sanskrit terms for the board's squares. The problem remains a standard teaching device for demonstrating exponential growth, geometric series and compound interest, because the doubling pattern grows so much faster than intuition expects.